prove that root 3 is irrational number?
BHOOPELLY SAIKUMAR , 8 Years ago
Grade 12th pass
Algebra> prove that root 3 is irrational number?
4 AnswersVikas TU
Last Activity: 8 Years ago
Suppose assume root3 is a rational number.
Then
root(3) can be expressed as: = p/q
where p,q are the integers.
then write,
p =qroot3
squaring both sides,
p^2 = 3q^2
Now for any integer (p,q)
the eqn. is not going to satify.
Therfore from the contradiction it gets untrue.
Hence it is not a rational number then therfore, it is a irrational number.
BHOOPELLY SAIKUMAR
Last Activity: 8 Years ago
prove that for all p,q that equation not satisfies.
and send post the answer . need proof for that,
how do I conclude that is not going to satisfy by directly telling so just post it
BHOOPELLY SAIKUMAR
Last Activity: 8 Years ago
WE NEED TO PROVE THAT FOR ALL P,Q SUCH THAT P2=3Q2 DOESN’T EXIST WHERE P,Q BELONGS TO Z. so justify ur answer with proper reason ….
mycroft holmes
Last Activity: 8 Years ago
P and Q are natural numbers, and hence in the prime factorization of P2 and Q2, every prime factor appears to an even power.
Now in the equation P2=3Q2 we have a contradiction as LHS has an even exponent for 3, whereas on RHS exponent of 3 is odd. So no such pair (P,Q) exists.
Hence 
is irrational
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